1. Field of the Invention
The invention relates to electromagnetic imaging of inhomogeneous, lossy targets having arbitrary shape, and in particular, it relates to microwave imaging to reconstruct electrical properties of biological tissue.
2. Statement of the Problem
Active microwave imaging for medical diagnosis is known in the art. U.S. Pat. No. 5,841,288, issued Nov. 24, 1998 to Meaney et al., discloses an apparatus and methods for determining electrical properties of an inhomogeneous target. The electrical property distribution on an arbitrary coarse mesh distribution of the target is first estimated; then corresponding electric field values on a fine mesh distribution of the target are computed. The fine mesh has finer discretization than the coarse mesh and is overlapping with the coarse mesh. Electric field values are then measured at preselected measurement sites within a homogeneous region external to the target. A Jacobian matrix is calculated, which represents a sensitivity calculation relative to a change in the electric field values at selected measurement sites due to a perturbation in the electrical property distribution on the coarse mesh. A difference vector is formed between the computed electric field and the measured electric field values, and an update vector is added to the electrical property distribution as a function of the difference vector and the Jacobian matrix. The electric field values are then re-computed based on the updated electrical property distribution, which is compared with the measured electric field values to produce a least squared error. If this error is not sufficiently small, the steps above, beginning with computing a Jacobian matrix, are repeated until the error is sufficiently small.
The dual mesh scheme reduces the number of points where electrical properties ∈r and "sgr" are calculated within a region of interest. The fine mesh is uniformly dense and is used for calculating the electric field values over the region; the coarse mesh is less dense, can be uniform or non-uniform, and is used for representing the k2 distribution within the region. The term xe2x80x9ck2xe2x80x9d is the complex wavenumber, squared, and includes both electrical properties ∈r and "sgr", (i.e., k2=xcfx89xcexc∈o∈r+jxcfx89xcexc"sgr", where ∈o is the dielectric constant in a vacuum, ∈r is the relative dielectric constant, "sgr" is the conductivity, and xcexc is the magnetic permeability of free space). The number of nodes on the coarse mesh is less than or equal to the number of individual pieces of measurement data. The dual mesh scheme thus utilizes a practical amount of measurement data and the calculation of the k2 distribution is performed without compromising the accuracy of the forward solution.
Such known methods and systems provide a calibration routine to convert 3-D measured data to a 2-D format. Such a routine is utilized because microwave antennae radiate into 3-D space; yet, the reconstruction algorithms typically utilize only 2-D radiation characteristics. This is important because of the nature of antennae: in 3-D, the free space loss factor (FSLF) varies proportionally to 1/R2 from the phase center of a transmitting antenna; while in 2-D, the FSLF varies proportionally to 1/R (R equals the distance from the phase center to the receiver). Thus, this approach substitutes the data""s dependency on 1/R2 with a dependency on 1/R. Specifically, a calibration routine calculates the phase center of each antenna and then modifies the amplitude relative to the 1/R2 and 1/R dependencies. The phase center is calculated by measuring the electric fields at a number of points within the homogeneous medium. A least squares procedure then determines where the phase center must have been to give such a field distribution.
In calculating the electrical property distribution of a target, the following equation is solved for the electric field vector, {overscore (E)}, at each iteration:
[A]{{overscore (E)}}={{overscore (b)}},
where [A] is the forward solution matrix, and {{overscore (b)}} is a vector representing the boundary condition. The derivative is then taken with respect to the electrical properties for every coarse mesh node i and every radiating transmitter antenna:             [                        ∂          A                          ∂                      k            i            2                              ]        ⁢          {              E        →            }        =            -              [        A        ]              ⁢                  {                              ∂            E                                ∂                          k              i              2                                      }            .      
Note that {{overscore (b)}} is not a function of the electrical property distribution so its derivative with respect to ki2 is zero. This equation is used to solve for       {                  ∂        E                    ∂                  k          i          2                      }    ,
since [A], {overscore (E)} are already known. A matrix   [            ∂      A              ∂              k        i        2              ]
is thus formed, in which its coefficients are the derivatives of the individual terms of the matrix [A] used in the forward solution of the electric fields. These coefficients are computed with respect to the electrical properties, ki2, at a single node on the coarse mesh. This new mesh, in combination with the original matrix [A] used in the computation of the electric fields and the most current calculated values of the electric field, {overscore (E)}, is used to compute the variations of the electric fields due to perturbation of the electrical properties, e.g.,       {                  ∂        E                    ∂                  k          i          2                      }    ,
at a single coarse mesh node, for a single radiator. The terms   {            ∂      E              ∂              k        i        2              }
make up the Jacobian matrix. Thus, to build the whole Jacobian matrix, the process is repeated for all of the radiators and all of the nodes. This time-consuming process can be efficiently done in parallel.
Typically, the inhomogeneous target object being analyzed is surrounded by a homogeneous medium contained in an illumination chamber. Transmitter and receiver antennae are disposed in the homogeneous region surrounding the object. Typically, the homogeneous medium is a saline bath or other liquid solution. Measuring the electric field includes irradiating the target with microwave energy having a single operating frequency from a plurality of transmitting antennae that surround the target, and receiving microwave energy at a second plurality of receiving antennae for each of the transmitting antennae. Typically, the antennae are arranged substantially within the same plane about the target. Computing the electric field includes computing, through simulation, the electric field at finite element nodes on the fine mesh. Determining electrical property distributions includes estimating the electrical property values based upon a homogeneous distribution with values identical to the homogeneous medium surrounding the target. Computing an electric field includes computing a two-dimensional field distribution utilizing hybrid element techniques. In such a technique, the electric field values are determined by finite element discretization of the target region and a small portion of the homogeneous region immediately surrounding the target region, in combination with the boundary element method to represent the outer surrounding homogeneous region. The step of discretizing the target with a finite element mesh (that is, the fine mesh) may include minimizing the number of nodes on the fine mesh.
An illumination chamber comprises material that is lossy within the operating frequency range, which is about 300 MHz to 1100 MHz in the prior art. The illumination chamber may have a thick solid wall, for example in a cylindrical or square shape, surrounding the target, and in which the antennae are disposed. Typically, however, the illumination chamber contains a liquid homogeneous medium, in which the target is disposed. Transmitting and receiving antennae are suspended within the liquid homogeneous medium to surround the target. Electrical property distributions are determined through a coarse mesh discretization of the illumination region, which includes the target region and homogeneous region. The fine mesh representing the target region is arbitrarily shaped.
Microwave imaging systems provide several advantages. First, they provide a method of determining the 2-D electrical property distributions of electrically nonuniform targets, which is relevant to the measure of human tissue due to the large contrast range of electrical properties. By way of example, bone and fat typically have a relative dielectric constant of about 5.0-6.0 at 500 MHz, while the dielectric constant of an aqueous based tissue (for example liver, kidneys and muscle) is more on the order of 50 to 70. The large contrast can be exploited in numerous applications, such as: 1) breast cancer detection, where the typical ex vivo breast tissue has a relative dielectric constant, ∈r, of about 15, while a malignant breast tumor has a relative dielectric constant, ∈r, in the range of 65-75; 2) the measurement of air and water content within tissue, because air has a dielectric constant, ∈r, of 1.0, and the dielectric constant, ∈r, of water is close to 75.
The spatial locations of the antennae surrounding a target must be precisely known to achieve accurate measurements of the electric field values and accurate computations with the finite element model. Preferably, the antennae are located all in a horizontal plane at a known vertical position. It is also important for the antennae to be able to reach and take measurements in positions suited to detect and measure electrical characteristics throughout the target object.
One of the complexities associated with realizing a viable medical microwave imaging system is the undesirable coupling of the imaging transceiver antennae with the surrounding environment (other than the biological target of interest). This problem is particularly acute in electronically scanned microwave arrays that typically consist of multiple transmit/receive antennae in close proximity. With the antenna array configurations typically utilized in the clinical interface in the art, the presence of non-active antennae perturbs the electromagnetic field patterns significantly, which can degrade the recovered images.
Also, electric field phase changes due to high contrast scattering by objects, like the breast, within the illumination region can often exceed xcfx80 radians. As a result, information may be lost with regards to the object under interrogation since conventional imaging schemes use the data and a format that restricts the range of possible phase values to the range of xe2x88x92xcfx80 to +xcfx80 radians.
Furthermore, exact dimensions of the target object, the target perimeter, at a given imaging plane are typically unknown. Data acquisition typically uses non-contacting antennae; thus, the target perimeter cannot be deduced accurately a priori, and this may compromise the accuracy of the calculations. In a typical method and apparatus of the prior art, a fine mesh is used for computing the electric field values at each iteration, and a course mesh is used for reconstructing the electrical properties within the target region. Because of typically high contrast in electrical properties between the surrounding saline solution and the target tissue, such a technique may be able to recover only an outline of the target and to achieve only minimal resolution of heterogenities within the target tissue. Essentially, the computational task of recovering the steep gradient at the target/saline bath interface overwhelms the more subtle task of recovering the map of a electrical property inhomogenities within the target tissue.
In methods and apparati for determining electrical properties of an inhomogeneous target, which include measuring electric field values external to a boundary that defines the target using an antenna array, in which an active transmitting antenna transmits a microwave signal, an active receiving antenna receives the microwave signal, and in which undesired coupling may occur between a nonactive antenna and the active antennas, improvements in accordance with the invention comprise methods and systems for compensating the coupling between the nonactive antenna and the active antennas.
Features of the invention include: modeling each nonactive antenna as an electromagnetic sink; presenting a matched termination to all nonactive antennae via a coaxial connection to either a coaxial matched load, a matched switch, or a well-matched amplifier; computing electric field values at the nonactive antennae; modeling the nonactive antennae as finite diameter cylinders having a surface, with a radiation type boundary condition imposed on the surface; empirically determining an effective radius and an effective impedance of the nonactive antennae. Empirically determining the effective radius and the effective impedance usually comprises measuring electric field values at a plurality of frequencies, preferably in a range of from 300 MHz to 3 GHz. Empirically determining the effective radius and the effective impedance typically includes measuring an electric field value when the nonactive antennae are present and when the nonactive antennae are not present.
In methods and apparati for determining electrical properties of an inhomogeneous target, including steps of measuring electric field values external to a boundary that defines the target using an antenna array having a plurality of antennae, in which an active transmitting antenna transmits a microwave signal, and an active receiving antenna receives the microwave signal, the invention provides an improvement including computing an amplitude and a phase value of the electric field values. Features of the invention include: unwrapping the phase value of the electric field values. Unwrapping the electric field values may include unwrapping of scattered computed 2D forward data. Unwrapping of scattered computed 2D forward data typically includes: calculating electric field values at a plurality of computation points between the antennae; choosing a reference computation point close to the active transmitting antenna; and comparing phase values at the computation point and a neighboring computation point to determine an unwrapped phase value at the neighboring computation point. Unwrapping the electric field values also typically include unwrapping scattered field data, which entails: determining a first unwrapped phase value at the active receiving antenna at a first, low frequency; measuring a second, wrapped phase value at the receiving antenna at a second, higher frequency; and then comparing the second, wrapped phase value with the first, unwrapped phase value to determine a second, unwrapped phase value. This procedure is repeated for all frequencies until the phases at all frequencies for each receiver have been unwrapped.
In determining electric field properties of an inhomogeneous target, including steps of measuring electric field values external to a boundary that defines the target, estimating electric property distributions in a coarse mesh discretization of the target, and computing an electric field in a fine mesh discretization of the target and at points external to the fine mesh discretization, the invention provides improvements including: performing a first reconstruction, thereby determining a perimeter of the target; and calculating a new fine mesh and a new coarse mesh, the new meshes conforming to the perimeter. In one aspect of the invention, the target is surrounded by a homogeneous medium, and the perimeter corresponds to an interface between the target and the homogeneous medium. The homogeneous medium typically is a saline bath. A target typically comprises biological tissue. Methods and apparati in accordance with the invention are particularly well-suited for determining electrical properties of a human female breast.
In methods and apparati for determining electric field properties of an inhomogeneous target, including steps of measuring electric field values external to a boundary that defines the target, estimating electric property distributions in a coarse mesh discretization of the target, and computing an electric field in a fine mesh discretization of the target and at points external to the fine mesh discretization, the invention provides an improvement including: using a Marquardt regularization scheme combined with a Tikhonov regularization scheme. Typically, the Marquardt scheme provides an initial guess of the electrical property distributions, and the Tikhonov scheme thereafter recovers a refined image of the electrical property distributions.
In systems and apparati for determining electrical properties of an inhomogeneous target, comprising an illumination chamber containing a homogeneous medium having substantially homogeneous electrical properties and in which the inhomogeneous target may be disposed, and an antenna array having a plurality of antennae disposed within the homogeneous medium for transmitting and alternately receiving microwave energy, the invention provides an improvement characterized in that the system comprises an A/D board capable of simultaneously sampling the downconverted signals received by a plurality of the antennae. Preferably, the system operates over a frequency band in a range of from 300 MHz to 3 GHz. The homogeneous region preferably comprises a saline solution. A system in accordance with the invention may comprise a microwave switching network for selecting one channel for signal transmitting and either one or multiple channels simultaneously for signal receiving. A system in accordance with the invention may comprise presenting a matched termination to all nonactive antennae via a coaxial connection to either a matched switch (as the last element of the switching matrix) or a single pole-double throw (SPDT) switch connected to a well-matched amplifier. A system may be further characterized in that the antenna array may comprise a plurality of inverted monopole antennae and in that the antenna array is movable to multiple vertical positions. Preferably, a system comprises an electronically controllable linear translation stage for vertically moving the antenna array. The antenna array may be mounted to a solid array plate. Preferably, the system comprises protective bellows for protecting electrical wires connected to the antennae. A system typically includes a sheet of solid material disposed above the homogeneous medium and the illumination tank, and having a hole for accommodating the inhomogeneous target. In particular, such a rigid sheet is capable of supporting a human patient and has a hole for accommodating a human body part.
Numerous other features, objects and advantages of the invention will become apparent from the following description when read in conjunction with the accompanying drawings.